{"title":"具有异质性传播的年龄感染结构人类免疫缺陷病毒模型的全局稳定性","authors":"Juping Zhang , Linlin Wang , Zhen Jin","doi":"10.1016/j.idm.2024.01.008","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we analyze the global asymptotic behaviors of a mathematical susceptible-infected(SI) age-infection-structured human immunodeficiency virus(HIV) model with heterogeneous transmission. Mathematical analysis shows that the local and global dynamics are completely determined by the basic reproductive number <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>. If <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo><</mo><mn>1</mn></math></span>, disease-free equilibrium is globally asymptotically stable. If <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>></mo><mn>1</mn></math></span>, it shows that disease-free equilibrium is unstable and the unique endemic equilibrium is globally asymptotically stable. The proofs of global stability utilize Lyapunov functions. Besides, the numerical simulations are illustrated to support these theoretical results and sensitivity analysis of each parameter for <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> is performed by the method of partial rank correlation coefficient(PRCC).</p></div>","PeriodicalId":36831,"journal":{"name":"Infectious Disease Modelling","volume":null,"pages":null},"PeriodicalIF":8.8000,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2468042724000083/pdfft?md5=507537c7b2bed62d58bb8bb2711eaa25&pid=1-s2.0-S2468042724000083-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Global stability for age-infection-structured human immunodeficiency virus model with heterogeneous transmission\",\"authors\":\"Juping Zhang , Linlin Wang , Zhen Jin\",\"doi\":\"10.1016/j.idm.2024.01.008\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, we analyze the global asymptotic behaviors of a mathematical susceptible-infected(SI) age-infection-structured human immunodeficiency virus(HIV) model with heterogeneous transmission. Mathematical analysis shows that the local and global dynamics are completely determined by the basic reproductive number <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>. If <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo><</mo><mn>1</mn></math></span>, disease-free equilibrium is globally asymptotically stable. If <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>></mo><mn>1</mn></math></span>, it shows that disease-free equilibrium is unstable and the unique endemic equilibrium is globally asymptotically stable. The proofs of global stability utilize Lyapunov functions. Besides, the numerical simulations are illustrated to support these theoretical results and sensitivity analysis of each parameter for <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> is performed by the method of partial rank correlation coefficient(PRCC).</p></div>\",\"PeriodicalId\":36831,\"journal\":{\"name\":\"Infectious Disease Modelling\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":8.8000,\"publicationDate\":\"2024-02-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S2468042724000083/pdfft?md5=507537c7b2bed62d58bb8bb2711eaa25&pid=1-s2.0-S2468042724000083-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Infectious Disease Modelling\",\"FirstCategoryId\":\"3\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S2468042724000083\",\"RegionNum\":3,\"RegionCategory\":\"医学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"Medicine\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Infectious Disease Modelling","FirstCategoryId":"3","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2468042724000083","RegionNum":3,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Medicine","Score":null,"Total":0}
Global stability for age-infection-structured human immunodeficiency virus model with heterogeneous transmission
In this paper, we analyze the global asymptotic behaviors of a mathematical susceptible-infected(SI) age-infection-structured human immunodeficiency virus(HIV) model with heterogeneous transmission. Mathematical analysis shows that the local and global dynamics are completely determined by the basic reproductive number . If , disease-free equilibrium is globally asymptotically stable. If , it shows that disease-free equilibrium is unstable and the unique endemic equilibrium is globally asymptotically stable. The proofs of global stability utilize Lyapunov functions. Besides, the numerical simulations are illustrated to support these theoretical results and sensitivity analysis of each parameter for is performed by the method of partial rank correlation coefficient(PRCC).
期刊介绍：
Infectious Disease Modelling is an open access journal that undergoes peer-review. Its main objective is to facilitate research that combines mathematical modelling, retrieval and analysis of infection disease data, and public health decision support. The journal actively encourages original research that improves this interface, as well as review articles that highlight innovative methodologies relevant to data collection, informatics, and policy making in the field of public health.
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